There's also not an Ellen May Cox born Oxford or Oxfordshire... hmm.
Ellen May McInnes died in 1964 aged 80 according to the WA bmd indexes - is this her? b. about 1884
You may need to check the information on the death certificates to see if it leads you to any further useful clues, as we're not turning up much right now.
You can order copies of certificate straight from WA:
http://www.bdm.dotag.wa.gov.au/H/how_to_obtain_a_certificate_from_the_index.aspx?uid=3998-7983-9731-6856Did your father have any siblings? (Please don't name them if they are still living, though). It would be unusual (although not impossible) for them to be married in 1912 but not have any kids until relatively late in life).
What year did Ellen come to Australia? Also, are you sure it's her, not another Ellen Cox, on that ship? It would also be worth looking for an Arthur McInnes (or similar name) on the same ship - perhaps they eloped, but never got around to an official wedding.